Solve for $x$ and $y$ using elimination. ${x+5y = 11}$ ${-x+4y = 7}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $9y = 18$ $\dfrac{9y}{{9}} = \dfrac{18}{{9}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {x+5y = 11}\thinspace$ to find $x$ ${x + 5}{(2)}{= 11}$ $x+10 = 11$ $x+10{-10} = 11{-10}$ ${x = 1}$ You can also plug ${y = 2}$ into $\thinspace {-x+4y = 7}\thinspace$ and get the same answer for $x$ : ${-x + 4}{(2)}{= 7}$ ${x = 1}$